Debreu’s social equilibrium theorem with asymmetric information and a continuum of agents

We provide several different generalizations of Debreu’s social equilibrium theorem by allowing for asymmetric information and a continuum of agents. The results not only extend the ones in Kim and Yannelis (J Econ Theory 77:330–353, 1977), Yannelis and Rustichini (Stud Econ Theory 2:23–48, 1991), but also new theorems are obtained which allow for a convexifying effect on aggregation (non-concavity assumption on the utility functions) and non-convex strategy sets (pure strategies). This is achieved by imposing the assumption of “many more agents than strategies” (Rustichini and Yannelis in Stud Econ Theory 1:249–265, 1991; Tourky and Yannelis in J Econ Theory 101:189–221, 2001; Podczeck in Econ Theory 22:699–725, 2003). To the memory of Gerard Debreu. A preliminary draft was presented in Paris, in April of 2005. I have benefited from the discussion, comments and questions of Erik Balder, Jean-Marc Bonnisseu, Bernard Cornet and Filipe Martins Da-Rocha and Conny Podczeck. A careful and knowledgeable referee made several useful comments and rescued me from a mishap.     

Detrimental externalities, pollution rights, and the “Coase theorem”

This paper, which builds on Chipman (The economist’s vision. Essays in modern economic perspectives, 131–162, 1998), analyzes a simple model formulated by Hurwicz (Jpn World Econ 7:49–74, 1995) of two agents—a polluter and a pollutee—and two commodities: “money” (standing for an exchangeable private good desired by both agents) and “pollution” (a public commodity desired by the polluter but undesired by the pollutee). There is also a government that issues legal rights to the two agents to emit a certain amount of pollution, which can be bought and sold with money. It is assumed that both agents act as price-takers in the market for pollution rights, so that competitive equilibrium is possible. The “Coase theorem” (so-called by Stigler (The theory of price, 1966) asserts that the equilibrium amount of pollution is independent of the allocation of pollution rights. A sufficient condition for this was (in another context) obtained by Edgeworth (Giorn Econ 2:233–245, 1891), namely that preferences of the two agents be “parallel” in the money commodity, whose marginal utility is constant. Hurwicz (Jpn World Econ 7:49–74, 1995) argued that this parallelism is also necessary. This paper, which provides an exposition of the problem, raises some questions about this result and provides an alternative necessary and sufficient condition.     

Ethnic fractionalisation, migration and growth

This paper has the aim of contributing to the existing research by analysing two particular topics. First of all, we show that the model specifications by Alesina et al. (J Econ Growth 8:155–194, 2003), which connects high ethnic fractionalisation to lower growth via bad policy variables, cannot fully explain the negative ethnic fractionalisation effect of the 1990s Sub-Saharan African growth experience. Moreover, we show that the remaining negative effect of ethnic fractionalisation on growth in Sub-Saharan Africa in the 1990s is due to an increased importance of adverse governance. Second, and on a very different note, we empirically investigate if ethnic fractionalisation might have a positive effect in a nation which is ethnically diverse due to immigration. There is evidence that it is important to distinguish between these two different kinds of ethnic fractionalisation.     

Capital growth in a global warming model: will China and India sign a climate treaty?

Global warming is now recognized as a significant threat to sustainable development on an international scale. One of the key challenges in mounting a global response to it is the seeming unwillingness of the fastest growing economies such as China and India to sign a treaty that limits their emissions. The aim of this paper is to examine the differential incentives of countries on different trajectories of capital growth. A benchmark dynamic game to study global warming, introduced in Dutta and Radner (J Econ Behav Organ, 2009), is generalized to allow for exogenous capital accumulation. It is shown that the presence of capital exacerbates the “tragedy of the common”. Furthermore, even with high discount factors, the threat of reverting to the inefficient “tragedy” equilibrium is not sufficient to deter the emissions growth of the fastest growing economies—in contrast to standard folk theorem like results. However, foreign aid can help. If the slower growth economies—like the United States and Western Europe—are willing to make transfers to China and India, then the latter can be incentivized to cut emissions. Such an outcome is Pareto improving for both slower and faster growth economies.     

Environmental tax policy in a model of growth cycles

Summary. The purpose of this paper is to consider environmental taxation which would control emissions of firms in a model of growth cycles. In the model presented below, the economy may experience two phases of growth and environmental quality: “the no-innovation growth regime” and “the innovation-led growth regime”. Aggregate capital and environmental quality remain constant in the no-innovation growth regime, while they perpetually increase in the innovation-led growth regime. The paper shows that the tax plays a key role in determining whether the economy stably converges to one of the two regimes or fluctuates permanently between them. It also shows that there is a critical level of the tax and that the economy obtains higher growth rates of capital and environmental quality by raising (or reducing) the tax if the initial tax is below (or above) the critical level. Received: April 2, 2001; revised version: March 21, 2002 RID="*" ID="*" This research reported here was conducted within the research project “Project on Intergenerational Equity” at Institute of Economic Research, Hitotsubashi University. I am deeply grateful to an anonymous referee for his or her insightful comments, which greatly improved the paper. I also thank Hiroshi Honda, Yasuo Maeda, Yuji Nakayama, and participants in workshops at Hitotsubashi University, Kyoto University, Nagoya University, Osaka University, University of Tsukuba, Yokohama National University, and University of Tokyo for their valuable comments and suggestions. Any remaining errors are mine.     

Graphical causal models and VARs: an empirical assessment of the real business cycles hypothesis

This paper assesses the empirical plausibility of the real business cycle view that shocks to real variables are the dominant sources of economic fluctuations and that monetary policy shocks play an insignificant role in determining the behavior of real variables. I reconsider the vector autoregressive model of King et al. (Am Econ Rev 81:819–840, 1991), but propose an alternative identification method, based on graphical causal models. This method selects the contemporaneous causal structure using the information incorporated in the partial correlations among the residuals. The residuals orthogonalization which follows and the study of the impulse response functions confirm the results of King et al. (Am Econ Rev 81:819–840, 1991): permanent productivity shocks are not the dominant sources of aggregate fluctuations in US economy. I would like to thank Peter Spirtes, Marco Lippi, and Clark Glymour for helpful comments on early versions of the paper. I am also grateful to Valentina Corradi for providing me with an updated version of the King et al. (1991) data set. The usual disclaimer applies.     

Strategic saving decisions in the infinite-horizon model

We study a mechanism that prevents the long-run distribution of wealth from becoming degenerate in the Ramsey–Cass–Koopmans model when households have different time-preference rates. This mechanism is based on the observation that price-taking behavior is no longer justified when all wealth is owned by a single household. Formalizing this observation, we obtain a model with a unique stationary equilibrium in which, depending on the parameter constellation, any number of households can own positive stocks of capital. We characterize this equilibrium and show for example that an increase in the dispersion of the time-preference rates across households unambiguously increases aggregate output. Whereas the main results are derived for a rather general class of production functions, we devote a separate section to the special case of the Cobb–Douglas technology for which the equilibrium conditions are particularly simple. The research reported in this paper forms part of the project “Economic Growth with Strategic Saving Decisions” supported by the Austrian Science Fund (FWF) under project number P17886. Comments from Robert Becker, Edward Green, Takashi Kamihigashi, David Levine, Fabrizio Zilibotti, anonymous referees, and participants at various conferences and seminars are gratefully acknowledged.     

Mapping prices into productivity in multisector growth models

Two issues related to mapping a multi-sector model into a reduced-form value-added model are often neglected: the composition of intermediate goods, and the distinction between the productivity indices for value added and for gross output. We illustrate their significance for growth accounting using the well known model of Greenwood et al. (in Am Econ Rev 87(3):342–362, 1997), who find that about 60% of economic growth can be attributed to investment-specific technical change (ISTC). We investigate the role of intermediate goods in their framework and find that, taking into account the composition of intermediates, ISTC may well account for between 93 and 96% of post-war US growth.     

Agreeing on generalised Darwinism: a response to Pavel Pelikan

Pelikan (J Evol Econ 21:341–366, 2011) develops an interesting conceptual framework that adds to prior work on generalised Darwinism. Despite claims to the contrary we show that it is similar to the approach developed by Hodgson and Knudsen (J Evol Econ 16(4):343–366, 2006a, J Econ Behav Organ 75(1):12–24, 2010a, b), Aldrich et al. (J Evol Econ 18(5):577–596, 2008) and others. Pelikan also mischaracterises the Hodgson–Knudsen position over Lamarckism. We show why the term is misleading (rather than strictly wrong) when applied to social evolution.     

Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium

In general rational expectations equilibrium (REE), as introduced in Radner (Econometrica 47:655–678, 1978) in an Arrow–Debreu–McKenzie setting with uncertainty, does not exist. Moreover, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayesian equilibrium of an extensive form game (Glycopantis et al. in Econ Theory 26:765–791, 2005). The lack of all the above properties is mainly due to the fact that the agents are supposed to predict the equilibrium market clearing price (as agent’s expected maximized utility is conditioned on the information that equilibrium prices reveal), which leads inevitably to the presumption that agents know all the primitives in the economy, i.e., random initial endowments, random utility functions and private information sets. To get around this problematic equilibrium notion, we introduce a new concept called Bayesian–Walrasian equilibrium (BWE) which has Bayesian features. In particular, agents try to predict the market-clearing prices using Bayesian updating and evaluate their consumption in terms of Bayesian price estimates, which are different for each individual. In this framework agents maximize expected utility conditioned on their own private information about the state of nature, subject to a Bayesian estimated budget constraint. Market clearing is not an intrinsic part of the definition of BWE. However, both in the case of perfect foresight and in the case of symmetric information BWE leads to a statewise market clearing; it then becomes an ex post Walrasian equilibrium allocation. This new BWE exists under standard assumptions, in contrast to the REE. In particular, we show that our new BWE exists in the well-known example in Kreps (J Econ Theory 14:32–43, 1977), where REE fails to exist. This work was done in the Spring of 2005, when EJB was a visiting professor at the University of Illinois.     

Schumpeter and the revival of evolutionary economics: an appraisal of the literature

During the last two decades we have seen a revival of interest in the works of Joseph Schumpeter and “evolutionary” ideas in economics more generally. A professional society honouring Schumpeter's name has been founded, and linked to it we have had for more than fifteen years now a professional journal devoted to this stream of thought. However, it has been argued that, despite these developments, the link between Schumpeter's own work and the more recent contributions to evolutionary economics is in fact rather weak. This paper considers this claim. Based on an analysis of Schumpeter's contribution to economics the paper presents an overview and assessment of the more recent literature in this area. It is argued that although there are important differences between Schumpeter's work and some of the more recent contributions, there nevertheless remains a strong common core that clearly distinguishes the evolutionary stream from other approaches (such as, for instance, so-called “new growth theory”). RID="*" ID="*" Many people have contributed to this paper in various ways. Jon Hekland at the Norwegian Research Council started it all by asking me to make an overview of the contribution from “evolutionary economics” to our understanding of contemporary economies. Several people helped me on the way by supplying written material, comments and suggestions, and I am indebted to all of them. Brian Arthur, Stan Metcalfe, Keith Pavitt, Erik Reinert, Paolo Saviotti and Bart Verspagen may be particularly mentioned. A preliminary version was presented at the conference “Industrial R&D and Innovation Policy Learning – Evolutionary Perspectives and New Methods for Impact Assessment” organised by the Norwegian Research Council (“SAKI”) at Leangkollen, Asker, April 18–19.2002. I wish to thank the discussant, Tor Jakob Klette, and the participants at the conference for useful feedback. Moreover I have benefited from comments and suggestions from the editors and referees of this journal. The final responsibility is mine, however. Economic support from the Norwegian Research Council (“SAKI”) is gratefully acknowledged.     

Are the antiglobalists right? Gains-from-trade without a Walrasian auctioneer

We show that the “fear” of globalisation can be rationalised by economic theory in the standard AD/AS equilibrium model, if we substitute the coordinational role of the Auctioneer by an implementation device based on learning (Guesnerie in Am Econ Rev 82, 1254–1278, 1992). When endowing producers with a learning ability to forecast market prices, individual profit-maximizing production decisions become interdependent in a strategic sense (strategic substitutes). Performing basic comparative statics exercises, we show that “competitiveness” matters in a precise sense: as foreign producers gain access to the home market, home producers’ ability to forecast market prices is undermined, so being their ability to forecast the profit consequences of their production decisions. A standard open economy exercise shows that the efficiency gains triggered by increased competition have to be traded-off against higher uncertainty (a lower likelihood to coordinate upon the welfare enhancing free-trade equilibrium). We interpret it as a new rationale for the existence of barriers to trade targeting coordination, rather than protecting mere inefficient sectors or industries (political economy driven). Finally, we show that classical measures evaluating ex-ante the desirability of economic integration (net welfare gains) do not always advice free trade. I wish to specially thank Roger Guesnerie, Thierry Verdier and an anonymous referee for their helpful suggestions. Comments by Facundo Albornoz, Pol Antràs, Gregory Corcos, Maurice Kugler, Robin Mason, Victor Norman, Emmanuel Ornelas and Susanna Thede are sincerely acknowledged. Audiences at the U. of Alicante, U. Autonoma de Barcelona, ETSG 2005 (Dublin), FGV-EPGE (RJ, Brazil), LACEA 2005 (Paris), the Miwest Trade Meeting at Minneapolis 2007, the Norwegian School of Economics (NHH), SBE 2005 (Natal, Brazil), U. of Southampton and T2M 2005 are acknowledged. The contents constitute chapter 4 of my PSE-EHESS PhD thesis, extended while I visited the NYU Economics department, sponsored by A. Bisin. Financial support from the Bank of Spain and CNRS is sincerely acknowledged.     

Endogenous structural change and crisis in a multiple time-scales growth model

The slow and endogenous twist of economic macro-structure makes up an important evolutionary feature of capitalist economies, and may be at the root of structural crisis. In this line, a Goodwinian growth model with increasing returns and profit-sharing that tries to picture a simple scenario of the seventies crisis is considered. It is shown that the exhaustion of the Kaldor-Verdoorn “productivity law” can entail, in a nonlinear framework, a “catastrophic” bifurcation from a “high” to a “low” growth path. Slow/fast dynamical systems then allow one to formalize a multiple time-scales dynamics where the growth path is shaped by the structural framework in which it takes place, but has also a long -un feedback. Structural change and crisis appear as long term and endogenous outcomes.     

Income inequality, democracy and growth reconsidered

Persson and Tabellini (Persson, T., Tabellini, G., 1992a. Growth, distribution and politics. Eur. Econ. Rev. 36, 593–602; Persson, T., Tabellini, G., 1992b. Growth, distribution and politics. In: Cukierman, A., Hercowitz, Z., Leiderman, L. (Eds.), Political Economy, Growth, and Business Cycles. MIT Press, Cambridge, MA, pp. 3–22; Persson, T., Tabellini, G., 1994. Is inequality harmful for growth? Am. Econ. Rev. 84, 600–621) as well as Alesina and Rodrik (Alesina, A., Rodrik, D., 1992. Distribution, political conflict, and economic growth. In: Cukierman, A., Hercowitz, Z., Leiderman, L. (Eds.), Political Economy, Growth, and Business Cycles. MIT Press, Cambridge, MA, pp. 23–50; Alesina, A., Rodrik, D., 1994. Distributive politics and economic growth, Q. J. Econ. 109, 465–490) have argued that income inequality reduces economic growth rates among democracies because it promotes distributional struggles. In this paper I question the supportive evidence for a number of reasons. Measures of income distribution and democracy are unreliable and permit only very tentative conclusions. Changes in data sources or recoding of some influential cases affect results. It is questionable whether equality effects on growth apply only within democracies, as a median voter interpretation of this relationship should make one expect. The general idea that distributional struggle hurts the growth prospects of nations, however, receives some empirical support.     

Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment

Summary. We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics. Received: September 13, 2001; revised version: December 9, 2002 RID="*" ID="*" We are grateful to Tapan Mitra for pointing out errors as well as making very valuable suggestions. Thanks are due to Raouf Boucekkine and Jorge Duran for additional helpful discussions. We also thank an anonymous referee for his/her helpful comments. The second author acknowledges the financial support of the Belgian Ministry of Scientific Research (Grant ARC 99/04-235 “Growth and incentive design”) and of the Belgian Federal Goverment (Grant PAI P5/10, “Equilibrium theory and optimization for public policy and industry regulation”). Correspondence to: C. Le Van     

Testing the balanced growth hypothesis: evidence from China

We investigate whether China’s experience during 1952–2004 supports the balanced growth entailment of the neoclassical growth model. Estimation of long-run relations among output, consumption and investment for the full period reject the balanced growth hypothesis for both the national and regional economies. When the economic reforms of the late 1970s are modelled as a structural break by the methods of Johansen et al. (Economet J 3(2):216–249, 2000) and Perron (Econometrica 57(6):1361–1401, 1989), we find some evidence of balanced growth in the pre-break period but in the post-break period the ‘great ratios’ are trend-stationary, precluding fully balanced growth, though permitting a common (stochastic) productivity trend.      

On Intersectoral allocations,factors substitutability and multiple long-run growth paths

Summary. This article considers a two-sector model of economic growth with “labour-augmenting” intersectoral external effects stemming from the aggregate capital stock. It is shown that equilibrium balanced growth paths with a non-trivial labour allocation scheme become available. A set of sufficient conditions for the existence of multiple equilibrium growth rays is provided and their determinacy properties are then characterised. Finally, examination of a parameterised C.E.S. economy illustrates the central role of non-unitary values for the elasticity of substitution in the multiplicity issue. Received: October 31, 2000; revised version: September 25, 2001     

Group contest success functions

This paper extends the axiomatic characterization of contest success functions of Skaperdas (Econ Theory 7:283–290, 1996) and Clark and Riis (Econ Theory 11:201–204, 1998) to contests between groups. Comments by Dan Kovenock significantly improved the paper and are gratefully acknowledged. I would also like to thank Pavlo Blavatskyy, Aron Kiss, Kai Konrad, Florian Morath, Dana Sisak, participants of the SFB/TR 15 meeting in Gummersbach 2004, the 2004 meeting of the Verein für Socialpolitik in Dresden, and two anonymous referees. Any errors are mine. Financial support from the Deutsche Forschungsgemeinschaft through SFB/TR 15 is gratefully acknowledged.     

Moments of truncated <Emphasis Type="Italic">t</Emphasis> and <Emphasis Type="Italic">F</Emphasis> distributions

Truncated distributions commonly arise in economics and related areas, see, for example, Lee (Econ Lett 3:165–169, 1979), Lien (Econ Lett 19:243–247, 1985; Econ Lett 20:45–47, 1986), Burdett (Econ Lett 52:263–267, 1996), Sercu (Insur: Math and Econ 20:79–95, 1997), Abadir and Magdalinos (Econom Theory 18:1276–1287, 2002), and Horrace (J Econom 126:335–354, 2005). In this note, we consider the most commonly encountered truncated distributions with heavy tails: the truncated t distribution and the truncated F distribution. For each of these distributions, we derive explicit expressions for the moments and estimation procedures by the method of moments and the method of maximum likelihood. An application is illustrated to a popular data set in the econometric literature.